MathDB
set of rationals not multiple of an $n$-th power of a prime

Source: JBMO 2008 Shortlist N2

October 14, 2017
JBMOnumber theory

Problem Statement

Let n≥2n \ge 2 be a fixed positive integer. An integer will be called "nn-free" if it is not a multiple of an nn-th power of a prime. Let MM be an infi nite set of rational numbers, such that the product of every nn elements of MM is an nn-free integer. Prove that MM contains only integers.
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